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Mesh free Galerkin method based on natural neighbors and conformal mapping

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Abstract

In this work, a robust mesh free method has been presented for the analysis of two dimensional problems. An efficient natural neighbor algorithm for construction of polygonal support domains has been used in this method that takes into account the nonuniform nodal discretization in the element free Galerkin formulation. The use of natural neighbors for determining the compact support is shown to overcome some of the shortcomings of the conventional distance metric based methods. For nonuniform nodal discretization there is a need for evaluating weights that have anisotropic compact supports. The smoothness and conformance of the weight function to the support domain obtained from natural neighbor algorithm is achieved through an efficient conformal mapping procedure such as Schwarz-Christoffel mapping. Numerical examples demonstrate that the proposed mesh free method gives good estimates of the stress/strain fields.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, 48109-2125, USA

    G. R. Balachandran

  2. Chair of Applied Mechanics, University of Erlangen Nuremberg, 91058, Erlangen, Germany

    A. Rajagopal

  3. Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, 600036, India

    S. M. Sivakumar

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  1. G. R. Balachandran
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  2. A. Rajagopal
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  3. S. M. Sivakumar
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Correspondence to S. M. Sivakumar.

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Balachandran, G.R., Rajagopal, A. & Sivakumar, S.M. Mesh free Galerkin method based on natural neighbors and conformal mapping. Comput Mech 42, 885–905 (2008). https://doi.org/10.1007/s00466-008-0292-0

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  • DOI: https://doi.org/10.1007/s00466-008-0292-0

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